A complete characterization of mixed state entanglement using probability density functions

• Main Authors: Bhardwaj, Shanthanu, Ravishankar, V
• Format: Journal Article
• Language: English
• Published: 02-03-2007
• Subjects: Physics - High Energy Physics - Theory; Physics - Other Condensed Matter; Physics - Quantum Physics
• DOI: 10.48550/arxiv.quant-ph/0703017

We propose that the entanglement of mixed states is characterised properly in
terms of a probability density function $\mathcal{P}(\mathcal{E})$. There is a
need for such a measure since the prevalent measures (such as
\textit{concurrence} and \textit{negativity}) are rough benchmarks, and not
monotones of each other. Considering the specific case of two qubit mixed
states, we provide an explicit construction of $\mathcal{P}(\mathcal{E})$ and
show that it is characterised by a set of parameters, of which concurrence is
but one particular combination. $\mathcal{P}(\mathcal{E})$ is manifestly
invariant under $SU(2) \times SU(2)$ transformations. It can, in fact,
reconstruct the state up to local operations
- with the specification of at most four additional parameters. Finally the
new measure resolves the controversy regarding the role of entanglement in
quantum computation in NMR systems.